the problem of finding the path between two points such that the transit time under specified conditions is minimized.

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Optimal tunnel shape for travelling inside the earth [duplicate]

Say you were to travel from Paris to Tokyo by digging a tunnel between both cities. If the tunnel is straight, one can easily compute that the time for travelling from one city to the other ...
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Why is a cycloid path the fastest way to roll a ball downward? [duplicate]

Possible Duplicate: Path to obtain the shortest traveling time I've been told that if one would want to make a ramp to get a ball from point A to a lower point B (at a certain horizontal ...
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Other kind of Brachistochrone problem

We know the Brachistochrone problem that to find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the ...
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What shape of track minimizes the time a ball takes between start and stop points of equal height?

I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end ...
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Brachistochrone problem for 3 points

I wonder how I can solve the Brachistochrone problem for 3 points? The matter starts from point A that is the highest point and it must pass from B and must finish with point C. (No any friction in ...
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Path to obtain the shortest traveling time

Asume we have a particle sitting at the point A(0,0) in a gravitational field. (g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0. What is the curve the particle ...
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Is there an intuitive reason the brachistochrone and the tautochrone are the same curve?

The brachistochrone problem asks what shape a hill should be so a ball slides down in the least time. The tautochrone problem asks what shape yields an oscillation frequency that is independent of ...
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Brachistochrone problem in general relativity

This question Brachistochrone Problem for Inhomogeneous Potential has the obvious extension. Namely the same question, when gravity is treated according to general relativity. To make it specific ...
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Brachistochrone Problem for Inhomogeneous Potential

This recent question about holes dug through the Earth led me to wonder: if I wanted to dig out a tube from the north pole to the equator and build a water slide in it, which shape would be the ...